A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems

Semi-analytic estimates of Lyapunov exponents in lower-dimensional systems

Statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable estimates of Lyapunov exponents χ in lower-dimensional Hamiltonian systems. This Letter explores the assumptions incorporated into these arguments. The predicted χ’s are insensitive to most details, but do depend sensitively on the nongeneric form of the auto-correlation function characte...

Degenerate Lower Dimensional Tori in Hamiltonian Systems

We study the persistence of lower dimensional tori in Hamiltonian systems of the form H(x, y, z) = 〈ω, y〉 + 1 2 〈z, M(ω)z〉 + εP (x, y, z, ω), where (x, y, z) ∈ T n × Rn × R , ε is a small parameter, and M(ω) can be singular. We show under a weak Melnikov non-resonant condition and certain singularity-removing conditions on the perturbation that the majority of unperturbed n-tori can still survi...

On the Normal Behaviour of Partially Elliptic Lower Dimensional Tori of Hamiltonian Systems

The purpose of this paper is to study the dynamics near a reducible lower dimen sional invariant tori of a nite dimensional autonomous Hamiltonian system with degrees of freedom We will focus in the case in which the torus has some elliptic directions First let us assume that the torus is totally elliptic In this case it is shown that the di usion time the time to move away from the torus is ex...

A KAM theorem without action-angle variables for elliptic lower dimensional tori

We study elliptic lower dimensional invariant tori of Hamiltonian systems via parameterizations. The method is based in solving iteratively the functional equations that stand for invariance and reducibility. In contrast with classical methods, we do not assume that the system is close to integrable nor that is written in action-angle variables. We only require an approximation of an invariant ...

Lindstedt Series for Lower Dimensional Tori